1. Field of the Invention
This invention relates to a compressor for compressing gas that operates as a fluid cooling medium in a refrigerating cycle machine and, more particularly, it relates to a liquid compressor comprising a helical blade.
2. Description of the Related Art
Various types of compressors are known including the "reciprocal type" and the "rotary type". Compressors of these known types, however, normally have a very complicated configuration including a drive unit and a compression unit, to which the turning effort of the drive unit is transmitted by means of one or more than one crank shafts of the drive unit, making the overall number of components and hence the manufacturing cost of the compressor considerable. Additionally, the rotary unit of such compressors is frequently off balanced and hence generates large noises.
In an attempt to solve these problems, fluid compressors comprising a helical blade have recently been proposed.
FIG. 16 of the accompanying drawings illustrates the compression unit of a known "helical blade type" fluid compressor. It comprises a cylinder 101, a turning body 102 which is slightly eccentrically located within and rotates relative to the cylinder 101 and a helical blade 104 fitted into and slidingly and radially movable in a helical groove 103 formed on the outer peripheral surface of the turning body 102.
The blade 104 slidingly and radially shifts its position in the groove 103 as the turning body 102 rotates relative to the cylinder 101. The opposites ends of the cylinder 101 and those of the turning body 102 are "freely rotatably" held by respective bearings 105 and 106. The bearings are respectively provided with a suction port 107 and a discharge port 108. Starting from the suction port 107, the pitch of the helix is gradually and progressively increases toward the discharge port 108 as a function of the distance from the suction port 107.
With such an arrangement, starting again from the suction port 107, the volumes of the spaces defined by the cylinder 101, the turning body 102 and the blade 104 gradually or progressively decrease toward the discharge port 108 as a function of the distance from the suction port 107. Thus, the operating fluid taken up by the unit through the suction port 107 is gradually compressed as it advances toward the discharge port 108 by the rotary movement of the turning body 102 until it is released from the discharge port 108.
With a fluid compressor having a compression unit having a configuration as described above, the "compression performance" of the unit are determined by the form and arrangement and of the groove 103 disposed on the peripheral surface of the turning body 102.
More specifically, the "compression ratio" of the fluid is determined by the ratio of the volume of the space closest to the suction port 107 to that of the space closest to the discharge port 108 regardless of the volumes of all the intermediate spaces defined by the cylinder 101, the turning body 102 and the blade 104. Therefore, in order for the compression ration to have a large value, it is necessary to make the volume of the space closest to the suction port 107 as large as possible relative to that of the space closest to the discharge port 10.
To meet the above requirement, conventional compressors typically have a blade holding groove 103 realized in a form as defined by the line graph of FIG. 17, (showing the relationship between the axial distance from the suction port 107 and the circumferential angle of the groove). In FIG. 17, the abscissa represents the circumferential angle .theta. of the groove 103 and the ordinate represents the distance Z from the suction port 107 of the turning body 102. The form of the groove consists of curve f and curve g. More specifically, the curve f is located closer to and convex toward the suction port 107 whereas the curve g is located closer to and convex toward the discharge port 108, the two different curves being linked at junction h. The fact that the suction port side curve f is convex toward the suction port 107 allows large spaces to be defined by the cylinder 101, the turning body 102 and the blade 104 near the suction port 107, contributing to the realization of a relatively large compression ratio.
Meanwhile, as the blade 104 goes in and out from (or, in other words, moves slidingly and radially in) the groove 103 of the turning body 102, groove is forced to deform the blade and consequently generates strain and stress inside of the blade. The generated strain and stress are distributed on the circumference direction of the blade 104. The inventors of the present invention conducted a mathematical analysis in a manner as described below as showing in FIGS. 21A to 21D to determine how strain and stress are generated in the blade as the blade is deformed in the helical groove of the turning body. If the blade initially has a helical form identical with that of the blade holding groove, no deformation can occur on the blade so long as the blade and the groove are coaxially arranged but the blade will be deformed to produce strain and stress in it once it is eccentrically disposed relative to the groove because the former is forced to conform to the shape of the latter. Assuming that there are a cylindrical coordinate system (R, .THETA., Z) with the Z-axis superposed on the center axis of the blade and another cylindrical coordinate system (r, .THETA., z) with the z-axis superposed on the center axis of the groove of the turning body and that the eccentrically of the two axis is expressed by e, a coordinate transformation can be carried out for either of the two coordinate systems by using the following equations if any eccentrically exists between the two systems. EQU Rcos.THETA.=rcos.theta.+e . . . (2-1) EQU Rsin.THETA.=rsin.theta. . . . (2-2)
Assuming that the Z-coordinate of the blade has an initial value of Z.sub.B before the blade is deformed and that the z-coordinate of the groove of the turning body has a value of z.sub.p, the displacement of the blade in the Z-direction, or .delta.Z, is expressed by the following equation. ##EQU1##
If the gradient of the groove is .gamma., the displacement of the blade in the direction perpendicular to its outer or upper surface, or .delta.Z.sub.B, is expressed as follows. EQU .delta.Z.sub.B =.delta.Zcos.gamma. . . . (2-4)
If the displacement of the inner periphery of the blade in the direction perpendicular to its outer or upper surface is .delta.Z.sub.Bi and the displacement of the outer periphery of the groove of the turning body in the direction perpendicular to its outer or upper surface is .delta.Z.sub.BO, they are respectively expressed by the following formulas. EQU .delta.Z.sub.Bi ={z.sub.p [Tan.sup.-1 {R.sub.i sin.THETA./(R.sub.i cos.THETA.-e)}]-Z.sub.B (.THETA.)}cos.gamma..sub.o . . . ( 2-5)
.delta.Z.sub.B0 ={z.sub.p [Tan.sup.-1 {R.vertline..sub.r=ro sin.THETA./(R.vertline.r=rocos.THETA.-e)}]-Z.sub.B (.THETA.)}cos.gamma..sub.o . . . ( 2-6)
where Ri is the inner diameter of the blade, ro is the outer diameter of the groove and R.vertline..sub.r=ro is the radial coordinate of the outer periphery of the groove in the cylindrical coordinate system of the blade when the blade is eccentric relative to the groove and expressed by ##EQU2##
If the blade is assumed as a circumferentially spread "straight beam", the bending surface strain .epsilon. of the blade is a function of the radius of curvature of beam deformation and expressed by the following formula.
.epsilon.==.+-.H/2.rho. . . . (2-8)
where H is the thickness of the blade and .rho. is a value expressed by the equation below, because the blade tangential direction coordinate T is expressed as T=R.THETA./cos.gamma.. EQU 1/.rho.=.differential..sup.2 .differential.Z.sub.B /.differential.T.sup.2. . . ( 2-10)
If .delta.Z.sub.B, .gamma. and R are discretely determined with an interval of .delta..THETA., the value of .rho. can be obtained by using the discrete values of these three points. Namely, EQU a=[(2R.sub.2 .delta..THETA./cos.gamma..sub.l-3).sup.2 +(.delta.Z.sub.B1 -.delta.Z.sub.B3).sup.2 ].sup.1/2 . . . ( 2-11) EQU A=Tan.sup.-1 [(R.sub.2 .delta..THETA./cos.gamma..sub.1-3)/(.delta.Z.sub.B2 -.delta.Z.sub.B1)]+Tan.sup.-1 [R.sub.2 .delta..THETA./cos.gamma..sub.1-3)/(.delta.Z.sub.B2 -.delta.Z.sub.B3)]. . . (2-12) EQU .rho..sub.2 =a/2sinA . . . (2-13)
Assuming that the initial gradient of the blade is .phi.(R,.THETA.) and the gradient angle of the groove is .phi.(r, .theta.), then the torsion displacement angle .delta..PHI. of the blade at its radial axis is expressed by the equation below. EQU .delta..PHI.=.phi.-.PHI. . . . (2-14)
Similarly, the torsion displacement angle .delta..PHI..sub.1 of the blade at its inner periphery and the torsion displacement angle .delta..PHI..sub.0 of the blade at its outer periphery are respectively expressed by the following equations. EQU .delta..PHI..sub.i .phi.(r.vertline..sub.R=Ri, Tan.sup.-1 {R.sub.i sin.THETA./(R.sub.i cos.THETA.-e)})-.phi.(R.sub.i, .THETA.) . . . (2-15) EQU .delta..PHI..sub.o =.phi.(r.sub.o, Tan.sup.-1 {R.vertline.r=ro.sup.sin.THETA./(R.vertline. r=ro.sup.cos.THETA.-e)})-.phi.(R.vertline.r=ro, .THETA.) . . . (2-16)
where ##EQU3##
The torsion angle .omega..sub.NT per unit length of the blade at its radial axis can be obtained by using the torsion displacement angle of the inner periphery of the blade, that of the outer periphery of the blade and the radial length .DELTA.R of the engaging area of the blade and groove. EQU NT=(.delta..PHI..sub.o -.delta..PHI..sub.i)/.DELTA.R . . . (2-18)
where
.DELTA.R=R.vertline..sub.r-ro-R.sub.i. The shear strain of the blade surface generated by the torsion, or .gamma..sub.NT, can be obtained from .omega..sub.NT above. EQU .gamma.NT=.+-.H.omega.NT/.sup.2 . . . ( 2-19)
If Z, R, .delta.Z are discretely determined with an interval of .delta..THETA., the value of .delta..PHI. can be obtained by using the discrete values of these two points. Namely, EQU .delta..PHI..sub.1 =Tan.sup.-1 [{(Z.sub.2 +.delta.Z.sub.2)-(Z.sub.1 +.delta.Z.sub.1) }/R.sub.1 .delta..THETA.]-Tan.sup.1 ((Z.sub.2 -Z.sub.1)/R.sub.1 .delta..THETA.} . . . (2-20)
According to a computation, a compressor of a known type provided with a groove defined by the line graph of FIG. 17 shows a circumferential direction distribution of bending strain as illustrated by the graph of FIG. 18.
It is apparent from FIG. 18 that the strain of the blade 104 reaches a maximum at the junction h of FIG. 17 where the two different component curves of the groove meet. Because of the very large strain to which the blade 104 is periodically subjected at the junction h of the two component curves when the turning body 102 is rotated, blades of the type under consideration are frequently damaged and broken at the junction h.
The forced deformation of the blade 104 also gives rise to a strain in it distributed radially and in the direction perpendicular to the principal surfaces of the blade 104, let alone a concentrated distribution of strain on the peripheries. According to a computation carried out by the inventors of the present invention, the bending strain generated by deformation of the helical blade of a conventional compression unit having a turning body with a groove defined by the line graph of FIG. 17 shows circumferential and radial distributions and a distribution in the direction perpendicular to the principal surfaces of the blade as illustrated respectively in FIGS. 18, 19 and 20.
It is seen from FIGS. 19 and 20 that the strain in the blade 104 shows a maximum also at a point on the inner periphery of the blade 104 that corresponds to the junction h of the two component curves and at points on the principal surfaces of the blade 104 corresponding to the junction h.
As described above, since conventional compressors are provided with a blade holding groove on the turning body having a form consisted of two component curves with a view to giving it a high compression ratio, they can periodically produce a large strain in the blade at locations corresponding to the junction of the two component curves when the burning body is rotated. Such a strain can eventually damage and break the blade.